A riming-dependent parameterization of scattering by snowflakes using the self-similar Rayleigh-Gans approximation

Riming is a key process of precipitation formation in ice-containing clouds, but quantifying riming from observations is challenging, limiting our ability to evaluate the riming process in numerical weather models. One challenge for radar observations is that riming changes both the physical properties (mass, area cross-section) and scattering properties of ice particles. These changes need to be implemented consistently as a function of riming in radar forward operators, which are required for retrievals and model evaluation in observation space. In this study, mass-size, cross-section area-size, and backscattering cross-section relations are developed as a function of the normalized rime mass for aggregates composed of various monomer types (columns, dendrites, needles, plates, and rosettes). The proposed framework allows us to simulate scattering properties of aggregated ice particles consistently as a function of riming in retrievals and radar forward operators. The parameterizations are developed from a large data set of simulated rimed aggregates of different sizes and monomer crystal types. The backscattering cross-section parameterization (the "riming-dependent parameterization") is evaluated for radar frequencies of 35.6 and 94.0 GHz and is based on the Self-Similar Rayleigh-Gans approximation (SSRGA), which is increasingly used to calculate microwave scattering of ice crystals and snowflakes. Compared with parameterizations from the literature that do not consider riming, the riming-dependent parameterization leads to significantly smaller biases in terms of backscattering cross-section. When using the particle masses and scattering properties of the individual particles simulated by the aggregation and riming model as a reference, the bias of our parameterization is below 1 dB when integrating over an exponential particle size distribution with sizes from 0.1-10 mm. In this study, a large data set of simulated rimed aggregates of different sizes and monomer shapes is used to develop a parameterization of the Self-Similar Rayleigh-Gans approximation (SSRGA) parameter by the normalized rime mass M$$ M $$ (the riming-dependent parameterization). We analyse the backscattering cross-section bias in the Ka and W bands using the riming-dependent parameterization and present mass-size and cross-section area-size relations for the generated particles depending on M$$ M $$. Applying the riming-dependent parameterization in combination with the mass-size relations presented leads to biases below 1 dB for both frequencies and all riming levels, assuming exponential size distributions.image